What is the integral of e^{(2x)/5} ?

The integral of e^{(2x)/5} is 5/2 e^{(2x)/5}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{(2x)/5}

\int e^{\frac{2 x}{5}} d x

\frac{5}{2} e^{\frac{2 x}{5}} + C

Solution steps

\int e^{\frac{2 x}{5}} d x

Apply u-substitution

= \int e^{u} \frac{5}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{5}{2} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{5}{2} e^{u}

Substitute back

u = \frac{2 x}{5}

= \frac{5}{2} e^{\frac{2 x}{5}}

Add a constant to the solution

= \frac{5}{2} e^{\frac{2 x}{5}} + C

What is the integral of e^{(2x)/5} ?
The integral of e^{(2x)/5} is 5/2 e^{(2x)/5}+C